Research On Improved Cubature Kalman Filter And Its Application In Navigation

This dissertation researches on improved cubature Kalman filter and its application in navigation.CKF is a kind of state estimation,which through sampling the state vector based on spherical-radial cubature rule and giving the same weights to obtain cubature points,to approximate the nonlinear Gauss system after passing by nonlinear functions.The filter algorithm is easy to realize since its high estimation accuracy and broad application prospects.The dissertation conducts an in-depth research on CKF,the main work is as follows:First of all,this dissertation researches on Cubature Kalman filter(CKF).On one hand,the derivation of the nonlinear filter recursive formula is given according to the minimum variance estimation criterion.On the other hand,this dissertation introduces the CKF derivation in detail.The comparative study of Unscented Kalman filter(UKF)and CKF shows that they are similar in the derivation process for comparative studies,but different in the Taylor expansion of higher order terms and numerical stability.CKF can accurately preserves the first-order moment and two order moments,which is better than UKF in the filtering precision in three dimension and above three dimensional nonlinear systems.Secondly,this dissertation researches on Augmented cubature Kalman filter(ACKF).ACKF is a kind of filtering method which can capture propagation statistical information in nonlinear filtering process,such as the average value of function,variance and odd order moment and so on,and get the Taylor expansion of the nonlinear function of mean.The study found that ACKF besides the mean and variance is more close to the true value,also can capture odd order moment information of communication part in addition,the precision is higher in the one-dimensional system;and the accuracy ACKF accuracy is worse than CKF owing to the greater error of its propagation statistical information in the two-dimensional and above systems.Conclusions of this research provide reference for the selection of different dimension of nonlinear system filtering method.Third,this dissertation researches on Strong tracking cubature Kalman filter(STCKF).Typically,the inertial devices constant drift can be regarded as a part of the state variables and estimated by the filter,but it is easily affected by the operating environment uncertainties and mutation.The stability decreases of CKF can come down due to the uncertainty of system mode,CKF does not have the robustness to overcome the uncertainty of system model,this dissertation has designed a kind of STCKF algorithm with suboptimal fading factor.Simulation results show that STCKF has strong tracking ability for the catastrophe of inertial device constant drift is robust to overcome the navigation system model uncertainty.Fourth,this dissertation researches on Adaptive cubature Kalman filter(ADCKF).In the noise statistics are unknown a priori or time-varying case,the accuracy of CKF filtering will decline or even divergence.The dissertation studied the ADCKF algorithm with a noise statistical estimator,according to the maximum a posteriori estimation theory.In inertial device random noise statistics in a hostile work environment is time-varying characteristics,the simulation results show that ADCKF need not precisely known the a priori statistical of inertial device random noise before filtring,and adaptive coping with inertial device random noise statistics change capacity.Finally,this dissertation researches on cubature Kalman filter and improved CKF used in the navigation system.The establishment of nonlinear error of INS model with the attitude and velocity error as the foundation,the CKF and its improved filtering algorithm(ACKF,STCKF,ADCKF)is applied to nonlinear system.The simulation results show that the improved filtering algorithm can solve the problem of observation equation cannot be accurately known case filter estimation problem.The superiority of improved filtering algorithm is more than CKF,with higher reliability,stronger practicability and better navigation accuracy.